My (20F) boyfriend (23M) did something behind my back and i’m not sure if I can trust him again

My boyfriend (23M) and I (20F) have been together for 6 months. Today we were at my apartment and I happened to glance over at his phone as he was scrolling through his text threads and I saw his ex was the third most recent person he had texted/received a text from. I didn’t mention it at first and waited about 5 minutes before asking if he was texting her to which he got quiet and nervously said yes. I asked why and again he took a second to think before responding “things”. I asked AGAIN why he was texting her and he said “my feelings about things” very nervously. From his reaction I could tell he knew he had just gotten caught doing something he shouldn’t have been doing. I said ok and walked to my bedroom and sat on my bed for about 5 minutes before he got up and came in to talk (not super relevant but I found it interesting he didn’t come in immediately, almost like he was thinking of a lie or deleting things).

He began explaining that he has been trying (“for a while” in his words) to text his ex for closure because when she broke up with him it was over text and there were some misconceptions around their breakup, one of them being cheating (she thinks he cheated because he hooked up with someone the day after she broke up with him, he claimed he wanted to explain to her what happened) along with he felt he never got closure and he didn’t like the fact that after the breakup they never had a conversation again. I started telling him how weird that was and how that’s how breakups work and you don’t always get closure and that’s life. I also told him that this should have been done prior to us meeting or dating which he agreed. I don’t want to get into the entire 2 hour long conversation but it was basically him saying he wanted to have one last phone call with her for closure and just to talk everything out one last time (he specifically said he didn’t know what he would say on the phone call he just wanted to have it because it would help him “close this door”). He also claimed he romanticized their three month long relationship and the breakup hit him hard, claimed he didn’t want her back because he didn’t want to lose me but just wanted closure, and said some other things i can’t remember anymore.

I told him I was going to message the girl on instagram myself and get her side of the store which he was apprehensive towards but agreed on. I messaged her but she never responded and as of right now the only version of events I have are his. I have virtually no trust in him as of now and don’t know if I want to believe what he told me or breakup with him even if he is telling the truth and it really was innocent. I never asked to see the messages because I didn’t want to cry or break down in front of him and I was hoping the girl would send me screenshots of his messages but never got a response so now I just have to trust his word. I don’t want breaking up to be the only option but I don’t know what to do at this point.

TL;DR: boyfriend texted his ex behind my back and now I’m not sure wether I can trust his version of events